2018

1. Identification in dynamic networks

   Paul M.J. Van den Hof, Arne G. Dankers, and Harm H.M. Weerts

   Computers & Chemical Engineering, 2018

   Abs DOI

   System identification is a common tool for estimating (linear) plant models as a basis for model-based predictive control and optimization. The current challenges in process industry, however, ask for data-driven modelling techniques that go beyond the single unit/plant models. While optimization and control problems become more and more structured in the form of decentralized and/or distributed solutions, the related modelling problems will need to address structured and interconnected systems. An introduction will be given to the current state of the art and related developments in the identification of linear dynamic networks. Starting from classical prediction error methods for open-loop and closed-loop systems, several consequences for the handling of network situations will be presented and new research questions will be highlighted.

2. Identifiability of linear dynamic networks

   Harm H.M. Weerts, Paul M.J. Van den Hof, and Arne G. Dankers

   Automatica, 2018

   Abs DOI

   

   Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we need to make sure that the network model set is identifiable. We introduce the notion of network identifiability, as a property of a parametrized model set, that ensures that different network models can be distinguished from each other when performing identification on the basis of measured data. Different from the classical notion of (parameter) identifiability, we focus on the distinction between network models in terms of their transfer functions. For a given structured model set with a pre-chosen topology, identifiability typically requires conditions on the presence and location of excitation signals, and on presence, location and correlation of disturbance signals. Because in a dynamic network, disturbances cannot always be considered to be of full-rank, the reduced-rank situation is also covered, meaning that the number of driving white noise processes can be strictly less than the number of disturbance variables. This includes the situation of having noise-free nodes.

3. Prediction error identification of linear dynamic networks with rank-reduced noise

   Harm H.M. Weerts, Paul M.J. Van den Hof, and Arne G. Dankers

   Automatica, 2018

   Abs DOI

   

   Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of identifying a dynamic network with known topology, on the basis of measured signals, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramér–Rao lower bound in the case of Gaussian noise. In order to reduce technical complexity, the analysis is restricted to dynamic networks with strictly proper modules.

2016

1. Identification of Dynamic Models in Complex Networks With Prediction Error Methods: Predictor Input Selection

   Arne Dankers, Paul M. J. Hof, Xavier Bombois, and Peter S. C. Heuberger

   IEEE Transactions on Automatic Control, Apr 2016

   Abs DOI

   

   This paper addresses the problem of obtaining an estimate of a particular module of interest that is embedded in a dynamic network with known interconnection structure. In this paper it is shown that there is considerable freedom as to which variables can be included as inputs to the predictor, while still obtaining consistent estimates of the particular module of interest. This freedom is encoded into sufficient conditions on the set of predictor inputs that allow for consistent identification of the module. The conditions can be used to design a sensor placement scheme, or to determine whether it is possible to obtain consistent estimates while refraining from measuring particular variables in the network. As identification methods the Direct and Two Stage Prediction-Error methods are considered. Algorithms are presented for checking the conditions using tools from graph theory.

2015

1. Errors-in-variables identification in dynamic networks — Consistency results for an instrumental variable approach

   Arne Dankers, Paul M.J. Van den Hof, Xavier Bombois, and Peter S.C. Heuberger

   Automatica, Apr 2015

   Abs DOI

   

   In this paper we consider the identification of a linear module that is embedded in a dynamic network using noisy measurements of the internal variables of the network. This is an extension of the errors-in-variables (EIV) identification framework to the case of dynamic networks. The consequence of measuring the variables with sensor noise is that some prediction error identification methods no longer result in consistent estimates. The method developed in this paper is based on a combination of the instrumental variable philosophy and closed-loop prediction error identification methods, and leads to consistent estimates of modules in a dynamic network. We consider a flexible choice of which internal variables need to be measured in order to identify the module of interest. This allows for a flexible sensor placement scheme. We also present a method that can be used to validate the identified model.

2013

1. Identification of dynamic models in complex networks with prediction error methods—Basic methods for consistent module estimates

   Paul M.J. Van den Hof, Arne Dankers, Peter S.C. Heuberger, and Xavier Bombois

   Automatica, Apr 2013

   Abs DOI

   

   The problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open-loop or closed-loop setting. In this paper, this problem is generalized to dynamical systems that operate in a complex interconnection structure and the objective is to consistently identify the dynamics of a particular module in the network. For a known interconnection structure it is shown that the classical prediction error methods for closed-loop identification can be generalized to provide consistent model estimates, under specified experimental circumstances. Two classes of methods considered in this paper are the direct method and the joint-IO method that rely on consistent noise models, and indirect methods that rely on external excitation signals like two-stage and IV methods. Graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent module estimates.

2012

1. On the Relationship Between the Enforced Convergence Criterion and the Asymptotically Optimal Laguerre Pole

   Arne G. Dankers, and David T. Westwick

   IEEE Transactions on Automatic Control, May 2012

   Abs DOI

   When approximating dynamic systems with Laguerre basis functions (LBFs) it is important to tune the Laguerre pole such that the expansion can be both parsimonious and accurate. Expressing the sum of squared errors (SSE) as a function of the Laguerre pole leads to an objective function that has many local minima and therefore cannot be optimized directly. Two alternative methods have been proposed in the literature: an asymptotically optimal method, and the enforced convergence criterion (ECC). In this paper, a generalization of the ECC will be investigated such that in the limit minimizing this generalized ECC and computing the asymptotically optimal solution lead to the same Laguerre pole. Moreover, it will be proved that these generalized ECCs are quasiconvex functions which means they can be efficiently minimized using numerical optimization techniques. The concept of operator quasiconvexity is investigated and used to prove quasiconvexity of the ECC.

2024

1. SYSDYNET - A MATLAB App and Toolbox for Dynamic Network Identification

   Paul M.J. Van den Hof, Shengling Shi, Harm H.M. Weerts, Xiaodong Cheng, Karthik R. Ramaswamy, Arne G. Dankers, Mannes H.J. Dreef, Stefanie J.M. Fonken, Tom R.V. Steentjes, and Job B.T. Meijer

   In 20th IFAC Symposium on System Identification, Jul 2024
2. Batched Decomposition Method for Behind-the-Fence Forecasting

   Gideon Egharervba, Arne Dankers, and Hamidreza Zareipour

   In 2024 IEEE PES Generation Transmission and Distribution in Latin America/ 2024 IEEE Power, Electronics and Computing Autum Meeting, Jul 2024

   accepted

2019

1. Generalized sensing and actuation schemes for local module identification in dynamic networks

   Karthik R. Ramaswamy, Paul M.J. Van den Hof, and Arne G. Dankers

   In 2019 IEEE 58th Conference on Decision and Control (CDC), Jul 2019
2. Local module identification in dynamic networks with correlated noise: the full input case

   Paul M.J. Van den Hof, Karthik R. Ramaswamy, Arne G. Dankers, and Giulio Bottegal

   In 2019 IEEE 58th Conference on Decision and Control (CDC), Jul 2019

2018

1. Dynamic Networks: Representations, Abstractions, and Well-Posedness

   N. Woodbury, A. Dankers, and S. Warnick

   In 2018 IEEE Conference on Decision and Control (CDC), Jul 2018
2. Single module identifiability in linear dynamic networks

   Harm H.M. Weerts, Paul M.J. Van den Hof, and Arne G. Dankers

   In 2018 IEEE 57th Conference on Decision and Control (CDC), Dec 2018

2017

1. From closed-loop identification to dynamic networks: generalization of the direct method

   P. M. J. Van den Hof, A. G. Dankers, and H. H. M. Weerts

   In Proceedings of the 56th IEEE Conference on Decision and Control, Dec 2017

   Submitted
2. On the Well-Posedness of Networks

   N. S. Woodbury, A. Dankers, and S. Warnick

   In Proceedings of the 56th IEEE Conference on Decision and Control, Dec 2017
3. Conditions for handling confounding variables in dynamic networks

   A. G. Dankers, P. M. J. Van den Hof, D. Materassi, and H. H. M. Weerts

   In Proceedings of 2017 IFAC World Congress, Dec 2017
4. Identification of dynamic networks with rank reduced noise

   Harm H.M. Weerts, Paul M.J. Van den Hof, and Arne G. Dankers

   In Proceedings of 2017 IFAC World Congress, Jul 2017
5. Prediction error identification with rank-reduced output noise

   Paul M.J. Van den Hof, Harm H.M. Weerts, and Arne G. Dankers

   In Proceedings of 2017 American Control Conference, May 2017
6. Identification in Dynamic networks

   Paul M.J. Van den Hof, Harm H.M. Weerts, and Arne G. Dankers

   In Foundations of Computer Aided Process Operations / Chemical Process Control (FOCAPO/CPC 2017), Jan 2017

2016

1. Blind Acoustic Source Separation via System Identification for Leak Detection in Pipelines

   A. Dankers, E. Jalilian, and D. Westwick

   IFAC Workshop on Adaptation and Learning Control in Signal Processing (ALCOSP), Jan 2016
2. Identifiability of dynamic networks with part of the node noise-free

   H.H.M. Weerts, P.M.J. Van den Hof, and A. Dankers

   IFAC Workshop on Adaptation and Learning Control in Signal Processing (ALCOSP), Jul 2016
3. Identification of dynamic networks operating in the presence of algebraic loops

   Harm H.M. Weerts, Paul M.J. Van den Hof, and Arne G. Dankers

   In 2016 IEEE 55th Conference on Decision and Control (CDC), Dec 2016

2015

1. Non-parametric identification in dynamic networks

   A Dankers, and P. M. J. Van den Hof

   In Proceedings of the 56th IEEE Conference on Decision and Control, Dec 2015
2. Identifiability in dynamic network identification

   H. H. M. Weerts, A. G. Dankers, and P. M. J. Van den Hof

   In Proceedings of the 17th IFAC Symposium on System Identification, Dec 2015

2014

1. An Instrumental Variable Method for Continuous-Time Identification in Dynamic Networks

   A. Dankers, P. M. J. Van den Hof, and X. Bombois

   In Proceedings of 53th Conference on Decision and Control (CDC), Dec 2014
2. Errors-in-Variables Identification in Bilaterally Coupled Systems with Application To Oil Well Testing

   M. Mansoori, A. Dankers, and P. M. J. Van den Hof

   In Proceedings of 19th IFAC World Congress, Dec 2014

   accepted
3. Errors in Variables Identification in Dynamic Networks by an Instrumental Variable Approach

   A. Dankers, P. M. J. Van den Hof, X. Bombois, and P. S. C. Heuberger

   In Proceedings of 19th IFAC World Congress, Dec 2014
4. A variance reduction technique for identification in dynamic networks

   Bilal Gunes, Arne Dankers, and Paul M.J. Van den Hof

   IFAC Proceedings Volumes, Dec 2014

2013

1. Predictor Input Selection for Two Stage Identification in Dynamic Networks

   A. Dankers, P. M. J. Van den Hof, X. Bombois, and P. S. C. Heuberger

   In Proceedings of the European Control Conference (ECC), Jul 2013
2. Predictor Input Selection for Direct Identification in Dynamic Networks

   A. Dankers, P. M. J. Van den Hof, and P. S. C. Heuberger

   In Proceedings of the 52nd IEEE Conference on Decision and Control (CDC), Dec 2013

2012

1. Dynamic Network Identification Using the Direct Prediction Error Method

   A. Dankers, P. M. J. Van den Hof, P. S. C. Heuberger, and X. Bombois

   In Proceedings of the 51st IEEE Conference on Decision and Control (CDC), Dec 2012
2. Identification in Dynamic Networks with Known Interconnection Topology

   P. M. J. Van den Hof, A. Dankers, P. S. C. Heuberger, and X. Bombois

   In Proceedings of the 51st IEEE Conference on Decision and Control (CDC), Dec 2012
3. Dynamic Network Structure Identification With Prediction Error Methods - Basic Examples

   A. Dankers, P. M. J. Van den Hof, P. S. C. Heuberger, and X. Bombois

   In Proceedings of 16th IFAC Symposium on System Identification, Jul 2012

2010

1. A Convex Method for Selecting Optimal Laguerre Filter Banks in System Modelling and Identification

   A. Dankers, and D. T. Westwick

   In Proceedings of the 2010 American Control Conference, Jul 2010

2006

1. Nonlinear System Identification Using Optimally Selected Laguerre Filter Banks

   A. Dankers, and D. T. Westwick

   In Proceedings of the 2006 American Control Conference, Jul 2006